To find the cosine of the angle between vectors t and r?

Question

when t = i - k
and r = i - j + k
keep getting zero in the denominator, is there another method, or have i got the components wrong, or does it mean something else ?!!?

Answer 1

The cross product of two vectors is always a vector.

If you get the zero vector - the sin of the angle is 0 which means that the angle is zero degrees.

You may have your math backwards - you should not get 0 in the denominator.

t and r are orthogonal vectors because their inner product is 0 but they are not perpendicular vectors.

The dot product in 2-space can be used to define perpendicular vectors because the angle between the two vectors must be 90 degrees. In 3-space, different ballgame.

Answer 2

The dot product of two vectors can be expressed as

t•r = | t | | r | cosθ
cosθ = (t•r) / { | t | | r | } = (1 + 0 - 1) / { | t | | r | } = 0
θ = 90°

The dot product of perpendicular vectors is always zero.

Answer 3

By defn. Vector t . Vector r = t r cosØ
0 = t r cos Ø
cos Ø = 0
Ø = 90°